Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D845 |
| unambiguous semidirect product | (C2×C5)⋊(C7×D169) |
| unambiguous semidirect product | (C2×C169)⋊(C7×D5) |
| Fitting | C2×C5×C7×C169 ⋊ C2 |
| derived, Hall | C5×C169 ⋊ C22×C7 |
| Hall | C5×C7×C169 ⋊ C22 |
| Hall | C7×C169 ⋊ C2×D5 |
| Sylow | C169 ⋊ C2×C7×D5 |
| Hall | C5×C7 ⋊ C2×D169 |
| Sylow | C5 ⋊ C2×C7×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D845 |
| commutator, cosocle, hypocenter | C5×C169 | C22×C7 |
| Frattini | C13 | C2×C7×D65 |
| Fitting | C2×C5×C7×C169 | C2 |
| socle | C2×C5×C7×C13 | D13 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 ◁ C2×C7 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11830 |
5936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 33);